The invention relates to a D/A converter, and more particularly to a R-2R D/A converter.
Data conversion techniques have been in existence for many years, and their use has become widespread. Converters used, such as a digital-to-analog (D/A) converter or an analog-to-digital (A/D) converter, have found homes in applications such as communication systems, consumer and professional audio, and precision measurement devices.
R-2R ladder network, a common approach applied in a D/A converter, uses fewer unique resistor values, thereby avoiding the requirement for several different precise input resistor values in other D/A converters. FIG. 1 shows a conventional n-bit R-2R D/A converter 10, comprising a R-2R ladder network 12 and an operational amplifier 14. The R-2R ladder network 12, coupled to reference voltage terminals, Vref+ and Vref−, receives an input digital code bIN=[bn-1 . . . . . b1 b0] to generate an analog output voltage Vout to the positive input of the operational amplifier 14. The output of the operational amplifier 14, Vout′, is coupled back to the negative input of the operational amplifier 04, wherein the operational amplifier 14 herein functions as a buffer. FIG. 2 shows the R-2R ladder network 12 in FIG. 1. The R-2R ladder network 12 comprises a plurality of series R resistors, parallel 2R resistors, and coupling switches, Sn-1 . . . S0. The last of the R resistors is coupled to a 2R terminating resistor 25 and the first R resistor is coupled to the output terminal. The 2R resistors are respectively coupled to the terminals of each series R resistor, wherein the first the 2R resistor is coupled to the output terminal and the last 2R resistor is coupled to the terminating resistor 25. Each coupling switch, Sn-1˜S0, selectively couples one corresponding 2R resistor to the reference voltage terminals, Vref+ or Vref−, in response to a corresponding digit of the input digital code bIN=[bn-1 . . . . . b1 b0]. For example, the coupling switch S0 couples the 2R resistor 21 to the reference voltage terminal Vref+ when b0=1, and Vref− when b0=0. If n=2, Vref+=1 (V), and Vref−=0 (V), the operation of conventional R-2R ladder networks follows with reference to FIGS. 3A and 3B. FIG. 3A and FIG. 3B show a 2-bit R-2R ladder network 32 with respect to different digital input code. As shown in FIG. 3A, the analog output voltage Vout is 0V when the input digital code bIN=[b1 b0]=[00]. In a similar manner, the analog output voltage Vout of FIG. 3 B=(Vref+−Vref−)*2R/(2R+2R)+Vref− is 0.5V when the input digital code bIN=[b1 b0]=[10].
However, element mismatch error in R-2R D/A converters due to manufacturing variation, imperfections in materials, changes in temperature, humidity, degradation and so on, degrades the performance thereof. For example, FIG. 3C shows a 2-bit R-2R ladder network 32 in the presence of element mismatch in the 2R resistor 31 (i.e. the resistance of resistor 31 is (2R+ΔR)). The resistance of the resistor 31 combining the terminating resistor 35 is then R′. When the digital code bIN=[10], the analog output voltage in FIG. 3C is {(Vref+−Vref−)*(R+R′)/[2R+(R′+R)]+Vref−}. Assuming R′=1.01R, the element matching ratio between the resistance of the resistor 33 and the resistance seen from node M is 2R/(R+R′)=1/1.005, thereby affecting the accuracy of the analog output voltage. Such element mismatching causes non-linearity problem in R-2R D/A converters, impacting both the DNL (Differential non-linearity) and monotonicity, especially when the input digital code is half full swing.
In the previous discussion, a 2-bit R-2R D/A converter is utilized to describe the principle of a R-2R ladder network; however, the operation is the same in a multi-bit R-2R D/A converter, such as a 10-bit R-2R D/A converter. FIG. 4 shows the output DNL of a 10-bit R-2R D/A converter-with 1% element mismatch error. The DNL is less than −1 (dB) when the input digital code is half swing (i.e. the input digital code is 512), where non-monotonic phenomenon exists when the DNL is less than −1 (dB). Further, the conductive resistance of switches in R-2R D/A converters also affects accuracy. Thus, it is desirable to have a R-2R D/A converter to overcome the described problems.